ELECTRIC CHARGE, FORCE AND FIELD (Young & Freedman Chap. 22) (Ohanian, Chaps. 22, 23) Brief review of electric charge and force

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1 EM 005 Handout : Electric Charge, orce and ield 1 ELECTRIC CHARGE, ORCE AND IELD (Young & reedman Chap. ) (Ohanian, Chaps., 3) Brief review of electric charge and force Recall: Atoms are composed of NEUTRONS, PROTONS and ELECTRONS Electrons and protons are subject to a force which does not affect neutrons To account for this force, electrons and protons are said to possess ELECTRIC CHARGE Opposite charges attract: e p Like charges repel: e p e p Convention: Electrons have NEGATIVE charge Protons have POSITIVE charge Note: 1. The sign of electric charge is NOT the same as mathematical sign. A different convention could easily have been adopted (e.g., North and South), or the electron could have been deemed positive and the proton negative.. The electron and proton have equal and opposite charges of ± e (the ELECTRONIC CHARGE) SI system: e = 1.60 x C (Coulombs - to be defined later) 3. A current of 1 Amp 1 Coulomb/second 6.3 x electrons/sec. This is a very large number so, macroscopically, we can regard

2 EM 005 Handout : Electric Charge, orce and ield charge as continuous rather than discrete. 4. Macroscopically, there are equal numbers of positive and negative charges, and they are well mixed. Therefore, electric forces tend to cancel out. This allows gravity, which is much weaker, to dominate. Ratio of electric and gravitational forces between an electron and a proton Elec. 39 =.3 x 10 Grav. Conductors and insulators Solid substances: Atoms are fixed in position. Nuclei and inner electrons cannot move. Outer electrons can be strongly or weakly bound Strongly bound INSULATOR (DIELECTRIC): even if an external electric force is applied, the electrons don t move. Loosely bound CONDUCTOR: electrons will move in response to an electric force, and so charge can flow. luid substances: Neutral particles Charged particles ELECTROLYTE = liquid conductor PLASMA = gaseous conductor insulator conductor: ionised atoms and free electrons can move about and carry a flow of charge Note: In questions on electrostatics, words like plastic, silk, paper etc. an insulator. Metal a conductor. As we shall see later, it is often important to remember whether a charged object is an insulator or a conductor.

3 EM 005 Handout : Electric Charge, orce and ield 3 Coulomb's law Consider two point charges, 1 and, with separation r Let = orce on due to 1 Magnitude of : Direction of : Let 1 = K 1 r rˆ be a unit vector pointing from 1 to 1 rˆ 1 r Then is along the direction of rˆ 1 is opposite to rˆ 1 if 1 and have the same sign if 1 and have the opposite signs The value of K depends on the system of units SI units: K = 8.99 x 10 9 N m C - or K 1 = where ε o = 8.85 x 10-1 N -1 m - C 4πε o ε o is the PERMITTIVITY CONSTANT or the PERMITTIVITY O REE SPACE So = ± 4πε 1 or rˆ 1 The Electric ield Coulomb's law in vector form Coulomb's law describes "action at a distance". This is valid for stationary charges (electrostatics), but not for charges in motion. Applying Coulomb's law directly in that case leads to violation of the law of conservation of momentum and the transmission of information faster than the speed of light. (See Ohanian p 591 for a good discussion of this point.) The concept of the ELECTRIC IELD gets around this problem.

4 EM 005 Handout : Electric Charge, orce and ield 4 Definition: The ELECTRIC IELD, E, at a point in space is equal to the force,, which a positive charge would experience at that point, divided by. i.e., E = Electric field orce per unit charge Note: 1. E is a VECTOR. The units of E are NC E is not a mathematical fiction: it is a REAL PHYSICAL ENTITY 4. Note the word "would" in the definition: E exists even if there is no charge present to experience it. To find E : ind the force on a positive "test charge", q, and divide by q. Magnitude : Given by Coulomb's Law Direction : Imagine how a small positive charge would move: that gives the direction of E Example: What is the electric field at distance r from a point charge? q E r r q rˆ 4 or = E rˆ πε 4 or = πε

5 EM 005 Handout : Electric Charge, orce and ield 5 Addition of electric forces and fields PRINCIPLE O SUPERPOSITION: The total force on a charge due to a number of other charges is given by the sum of all the forces on it due to the individual charges. The same applies to addition of electric fields. i.e., Electric forces and fields are added as VECTORS Example: A system of three charges r 1-1 Resultant force on is 1 = 1 + r + Where 1 = orce due to 1 = orce due to In general, for a system of n other charges acting on a charge, the total force on is 1 = n 1 i 4πεor rˆ i etc. etc r i r r 3 i 3

6 EM 005 Handout : Electric Charge, orce and ield 6 Examples of Electrostatic orce Calculations 1. A system of three point charges in the X-Y plane. An electric dipole 3. Electric field on the axis of a line of charge 4. Electric field on the axis of a charged ring See lecture notes

7 EM 005 Handout : Electric Charge, orce and ield 7 Electric field lines E is represented graphically by ELECTRIC IELD LINES ield lines start at positive charges and end at negative charges The direction of a field line at any point is the direction of E at that point The density of lines is proportional to the magnitude of E Lines do not intersect except at charges ield lines are NOT real - they just help us to visualise the field Convention: /ε o field lines originate from a charge Examples: using the field lines concept to find the electric field 1. E due to an infinite plane sheet of uniform charge density. E due to an infinite line of uniform charge density See lecture notes

8 EM 005 Handout : Electric Charge, orce and ield 8 An electric dipole in an electric field Recall: an ELECTRIC DIPOLE two equal and opposite charges separated by a fixed distance. Although it is electrically neutral, it will be influenced by an electric field because the charges are separated. - L θ E Consider a dipole (±, separation L) in a uniform electric field, and let the dipole axis be at an angle θ to the field direction, as shown. Charge experiences a force as shown, with magnitude Charge - experiences a force as shown, with magnitude = E = E The two equal and opposite forces have different lines of action, and so generate a TORUE, τ. rom the diagram, the torque tends to rotate the dipole so as to reduce θ - i.e., to align the dipole axis with the field. Convention: Positive torque tends to increase θ (anticlockwise rotation) Negative torque tends to decrease θ (clockwise rotation) By definition, Torque = (orce)(perpendicular distance between lines of action) in this case, τ = -ELsinθ Recall: L = Dipole Moment, P τ = -PEsinθ This looks like the magnitude of a VECTOR CROSS PRODUCT, and it is. The torque is a vector defined as τ = P E P is the ELECTRIC DIPOLE MOMENT VECTOR Direction of P : rom the negative charge towards the positive charge Direction of τ : By the right hand rule, τ is perpendicular to both P and E (into the page as drawn here). P θ τ (inwards) E

Eðlisfræði 2, vor 2007

[ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 28. Sources of Magnetic Field Assignment is due at 2:00am on Wednesday, March 7, 2007 Credit for problems submitted late will decrease to 0% after the deadline